I am trying to develop a short course on financial theory, covering the fundamentals of forward and options pricing, and 'efficient market' theory. I want to reduce the amount of mathematics to a minimum. This is not because the audience does not include mathematicians (it does) but rather because in my view mathematics generally detracts from the simplicity and beauty of a subject. Mathematics also focuses on the process of derivation from assumptions, rather than the assumptions themselves.

My question is whether this would be possible for financial theory. In particular (a) are there any basic principles of financial theory that cannot be grasped without complex mathematics and (2) are there any important results (i.e. derived results) which cannot be explained except by complex mathematics?

You realize that it doesn't have to be that way. Mathematics are a tool that allows you to formalize and be precise about what you mean. I personally understand any concept much better when someone writes some math. Before than that, everything looks fuzzy or arbitrary. Mathematics are a great tool to have and understand, and I feel that is responsibility of the professor to translate that intuition to mathematics. In other words, if you can explain something without the maths, you can explain the same with the maths (unless you don't understand them) and it will be even better.
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FKariaFeb 13 '14 at 0:27

Thank you Anna. I also found "Understanding N(d1) and N(d2): Risk-Adjusted Probabilities in the Black-Scholes Model" by Lars Tyge Nielsen very helpful. (Revue Finance (Journal of the French Finance Association) 14 (1993), 95-106. ltnielsen.com/wp-content/uploads/Understanding.pdf ). This has a neat explanation of what d1 and d2 are, which I always found a bit of a mystery.
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quis est illeFeb 12 '14 at 15:13

Reminded me there was a time when the professor insisted a guy to describe the algorithm in form of a "Formula" - my friend wrote pseudo code
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user7228Feb 13 '14 at 16:11

My primary objective in a book like this is to create something about
derivatives that is easy to read. Derivatives can be a painful subject
to learn, and many legal pads are used up, sometimes frustratingly, in
working through some of the principles covered in technical
derivatives books. This book is different. While I do not advise that
you curl up with it by a warm ﬁre, a loyal dog, and a loved one, I do
think you can relax in an easy chair and read it without pen and paper
at your side. To that extent, this book is unique. Rarely will you ﬁnd
a derivatives book without equations.

@Anna: I haven't seen you before here, so a very warm welcome to you! What is your background? I see that you are located in Frankfurt. I am a professor in Aschaffenburg, near Frankfurt. If you would like to expand your quant network you can drop me a line here: h-ab.de/nc/eng/…
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vonjdFeb 12 '14 at 19:08

1

@vondj Thanks, I will.
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user1157Feb 12 '14 at 19:18

1

I feel compelled to read any book with a chapter called "Why the Expected Return Is Not To Be Expected".
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quis est illeFeb 13 '14 at 10:45